Persistent homology was originally introduced as a method to encode in a single object the evolution of the homology of a family of nested cell complexes (usually simplicial complexes) parametrized by a linearly ordered set of indexes, such as the integers or the reals [1]}, [2]}, [3]}, [4]}. Later it became clear that families of nested complexes parametrized over other sets of indices can be equally relevant (see, e.g., [5]} for a review). In particular, multi-persistence [6]} treats the case of integer parameters along multiple directions, that is a grid. This is the setting we consider here.
